The student will find the change in altitude of the Sun and the Moon over the
course of the year. They will explore the relationship between the altitude
of the Sun and the length of the daylight hours.
Background and Theory
Sally is the sort of person who finds the darkness of fall and winter very
depressing. In order to cheer her up in the wintertime, you make a chart of
the transit altitude of the sun over the course of the year, and show that
this is related to the length of the day. Now she can tell right away whether
things are getting worse or better, and how long she has to wait before she
will be happy again!
One more thing about Sally: she's a bit odd. Her neighbors all know how much
Sally loves to howl into the night whenever the moon is full. On the same
chart, you indicate the dates of the full moon in each lunar cycle, and, for
those dates, the altitude of the moon at transit. Now she can PLAN to drive
the neighbors crazy!
Procedure

In Table 1 on the worksheet, fill in the rise time, set time, and altitude (h) of the Sun at transit. Do this for the same day of each month, from the current month in the current year to the same month next year.

Calculate the length of daylight from the data in your table. Express this in hours and minutes for each month.

Collect the lunar information. Scroll down the table until you find a full moon icon (solid white disk). Usually there are several days in a row with this icon. Find the day when the transit occurs closest to midnight (or 1 am during Daylight Savings Time!). This is the day of the full moon. (Why?)

Record the date, and the transit altitude (h) of the moon in Table 2.

Plot the altitude of the Sun at transit versus the date for one full year. Connect your data points with a smooth line.

On the same graph, in a different color, plot the length of the day versus date. Connect your data points with a smooth line.

In a third color, plot the altitude of the Full Moon at transit versus date over one year. Connect your data points with a smooth line.

Label the summer solstice, winter solstice, vernal and autumnal equinoxes. Use your graph to show that the length of the day changes fastest near the equinoxes.

Your graphs should be annotated with any other explanations and comments of interesting phenomena that you notice.